Question

Write the equation of a line that passes through the points (1, 5) and (2, 7).

A. y = 2x + 3
B. y = 2x + 5
C. y = 3x + 2
D. y = 3x + 4

Answer 1

The equation of a line that passes through the points (1, 5) and (2, 7) is y = 2x + 3.

Step-by-step explanation:

The equation of a line that passes through two points can be found using the formula:

`y - y_1 = m(x - x_1)`

Where (x1, y1) are the coordinates of one point, and m is the slope of the line. To find the slope, we can use the formula:

`m = (y_2 - y_1) / (x_2 - x_1)`

Using the given points (1, 5) and (2, 7), we can substitute these values into the formula and simplify to find the equation:

`y - 5 = (7 - 5) / (2 - 1)(x - 1) y - 5 = 2(x - 1) y - 5 = 2x - 2 y = 2x + 3`

Therefore, the equation of the line that passes through the points (1, 5) and (2, 7) is option A, y = 2x + 3.